Abstract-Extended orthogonal space time block coding (EO STBC) can achieve high transmit diversity over a multiple input mUltiple-output (MIMO) channel. To do so, it requires channel state information on the transmitter side, which needs to be estimated and fed back from the receiver. Therefore, this paper explores an estimation and tracking scheme by means of a Kalman ilter, which is integrated with EO-STBC detection and exploits the smooth evolution of the channel coeicients by applying differential feedback. For slow fading, we propose the inclusion of a drit vector in the Kalman model, which is motivated by a second order approximation of the underlying channel model and can be shown to offer advantages in terms of temporal smoothness when addressing channels whose coeicient trajectories evolve smoothly.